This invention relates to investigation of rocks and other porous materials, and, more particularly, to nuclear magnetic resonance (NMR) methods and apparatus for determining pore characteristics of such substances either in the laboratory or in situ in earth formations.
General background of nuclear magnetic resonance (NMR) well logging is set forth, for example, in U.S. Pat. No. 5,023,551. Briefly, in conventional NMR operation the spins of nuclei align themselves along an externally applied static magnetic field. This equilibrium situation can be disturbed by a pulse of an oscillating magnetic field (e.g. an RF pulse), which tips the spins away from the static field direction. After tipping, two things occur simultaneously. First, the spins precess around the static field at the Larmor frequency, given by xcfx890=xcex3B0, where B0 is the strength of the static field and xcex3 is the gyromagnetic ratio. Second, the spins return to the equilibrium direction according to a decay time T1, which is called the longitudinal relaxation time constant or spin lattice relaxation time constant. For hydrogen nuclei, xcex3/2xcfx80=4258 Hz/Gauss, so, for example, for a static field of 235 Gauss, the frequency of precession would be 1 MHz. Also associated with the spin of molecular nuclei is a second relaxation time constant, T2, called the transverse relaxation time constant or spin-spin relaxation time constant. At the end of a ninety degree tipping pulse, all the spins are pointed in a common direction perpendicular to the static field, and they all precess at the Larmor frequency. The net precessing magnetization decays with a time constant T2 because the individual spins rotate at different rates and lose their common phase. At the molecular level, dephasing is caused by random motions of the spins. The magnetic fields of neighboring spins and nearby paramagnetic centers appear as randomly fluctuating magnetic fields to the spins in random motion. In an inhomogeneous field, spins at different locations precess at different rates. Therefore, in addition to the molecular spin-spin relaxation of fluids, spatial inhomogeneities of the applied field also cause dephasing. Spatial inhomogeneities in the field can be due to microscopic inhomogeneities in the magnetic susceptibility of rock grains or due to the macroscopic features of the magnet.
A widely used technique for acquiring NMR data, both in the laboratory and in well logging, uses an RF pulse sequence known as the CPMG (Carr-Purcell-Meiboom-Gill) sequence. As is well known, after a wait time that precedes each pulse sequence, a ninety degree pulse causes the spins to start precessing. Then a one hundred eighty degree pulse is applied to cause the spins which are dephasing in the transverse plane to refocus. By repeatedly refocusing the spins using one hundred eighty degree pulses, a series of xe2x80x9cspin echoesxe2x80x9d appear, and the train of echoes is measured and processed. The transverse relaxation time constant, T2, or the distribution of T2""s, can be obtained using this technique.
Examination of porous substances is treated herein. Although porous materials appear in almost every aspect of the environment from naturally occurring rocks and woods to man-made materials such as concrete and food products, the characterization of the internal geometry of such materials remains difficult. Statistical description of the pore space is often most useful in understanding the physical properties of the materials, such as permeability to fluid flow. One of the most important statistical parameters is the linear dimension (d) characterizing the pore size. Nuclear magnetic resonance technique has been successfully used to measure the surface-to-volume ratio ( less than S/V greater than ) of porous materials via spin relaxation (see W. E. Kenyon, Nucl Geophys. 6, 153, 1992; R. L. Kleinberg, in xe2x80x9cEncyclopedia of Nuclear Magnetic Resonancexe2x80x9d, Wiley, N.Y., 1995) and to study pore structure using pulsed field gradient (pfg) techniques (see E. O. Stejskal and J. E. Tanner, J. Chem. Phys. 42, 288, 1965; P. T. Callaghan, A. Coy, D. MacGowan, K. J. Packer and F. O. Zelaya, Nature 351, 467, 1991). From the measurement of  less than S/V greater than , one may deduce a pore size "igr", as: "igr"xe2x89xa16/ less than S/V greater than . This general methodology has been successful in characterizing sandstone formations. However, in materials with complex surface relaxivity, such as due to microporosity, clay and deviation from fast diffusion condition, the interpretation of the spin relaxation behavior may be complex and model-dependent.
It is among the objects of the present invention to provide improved technique and apparatus for characterizing the internal geometry of porous materials using nuclear magnetic resonance measurements.
When a porous material is subject to a uniform external magnetic field (Bo), an inhomogeneous magnetic field Bi may appear inside the pore space, due to the contrast of the magnetic susceptibility ("khgr") between the solid materials and the pore-filling fluid. One may estimate the magnitude of the internal field to be Bixcx9cxcex94"khgr"Bo, where xcex94"khgr" is the difference in susceptibilities. The inhomogeneity of this internal field can be rather large in sedimentary rocks (xcex94"khgr"xcx9c10xe2x88x924-10xe2x88x926 (SI)) (see M. D. Hurlimann, J. Magn. Res. 131, 232-40, 1998) and cause problems in the measurements of diffusion constant and spin relaxation (see E. L. Han Phys. Rev. 80, 580, 1950; E. O. Stejskal and J. E. Tanner, J.Chem Phys. 42, 288, 1965; R. M. Cotts, M. J. R. Hoch, T. Sun and J. T. Markert, J. Magn. Res. 83, 252, 1989).
The present invention utilizes to advantage the fact that the internal magnetic field is a representation of the underlying geometry of a porous material. The spatial distribution of the internal field can be a measure of the pore geometry. A technique is set forth to characterize the decay of nuclear spin magnetization due to diffusion in the internal field (DDif) and define a length scale "igr"DDif (corresponding to pore size) in terms of the diffusion behavior. The technique has been used to study the water diffusion in samples of random-packed beads of several sizes and sedimentary rock samples, which demonstrated the utility of the approach.
A significant aspect of the technique hereof is that it is insensitive to relaxation, so it provides a conceptually different characterization of porous materials from the widely used spin relaxation method. Particularly in cases where the spin relaxation is dominated by the inclusion of clay, microporosity, wettability and other types of variation of surface relaxation, the spin relaxation method is not reliable in determining physical properties such as permeability. [Carbonate rock has provided an example showing that the interpretation of relaxation data may be difficult and model dependent (see T. S. Ramakrishnan, L. M. Schwartz, E. J. Fordham, W. E. Kenyon, D. J. Wilkinson, SPWLA, 1998).]
In accordance with an embodiment of the method of the invention, there is provided a technique for determining a pore characteristic of a substance, comprising the following steps: subjecting the substance to a substantially uniform static magnetic field; applying a magnetic pulse sequence to the substance, the pulse sequence being selected to produce nuclear magnetic resonance signals that are responsive to internal magnetic field inhomogeneities in the pore structure of the substance, and detecting, as measurement signals, nuclear magnetic resonance signals from the substance; applying a reference magnetic pulse sequence to the substance, the reference pulse sequence being selected to produce nuclear magnetic resonance signals that are substantially unresponsive to internal magnetic field inhomogeneities in the pore structure of the substance, and detecting, as reference measurement signals, nuclear magnetic resonance signals from the substance; and determining a pore characteristic of the substance from the measurement signals and the reference measurement signals.
In a preferred embodiment of the invention, the step of determining a pore characteristic of the substance comprises dividing values derived from the measurement signals by values derived from the reference measurement signals. In this embodiment, the step of applying a magnetic pulse sequence comprises applying a plurality of pulse sequences that include respective different wait times, td, during which diffusion in the internal magnetic field inhomogeneities can occur. Also in this embodiment, each of the pulse sequences comprises a series of pulse sequences with phase cycling, and the measurement signals for each of said plurality of pulse sequences are obtained by combining the detected nuclear magnetic resonance signals from the associated series of pulse sequences. Also in this embodiment, the step of determining a pore characteristic includes plotting the results of the previously mentioned dividing as a function of td, and determining the pore characteristic from said plot.
Further features and advantages of the invention will become more readily apparent from the following detailed description when taken in conjunction with the accompanying drawings.